1. **Problem statement:** We have a right triangle with sides opposite to angle $\theta$ as 3, adjacent to $\theta$ as 4, and hypotenuse as 5. We need to find $\cos(\theta)$.\n\n2. **Formula:** The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$\n\n3. **Apply the values:** Here, adjacent side = 4 and hypotenuse = 5, so $$\cos(\theta) = \frac{4}{5}$$\n\n4. **Simplify:** The fraction $\frac{4}{5}$ is already in simplest form.\n\n5. **Conclusion:** Therefore, the value of $\cos(\theta)$ is $$\boxed{\frac{4}{5}}$$.